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The risk library  /  What a risk costs

Art. 04 · What a risk costs · 3 min read

Putting probabilities in context

"A 0.4% annual chance" tells you nothing. Restated as a waiting time, the same fact becomes a decision.

People are poor at raw probabilities and surprisingly good at comparisons. Nobody has an intuition for 0.4%. Everybody has an intuition for "about once in every 250 years, so probably not in the lifetime of this building, but it happens somewhere in the country every week."

Three translations do most of the work:

Into waiting time. Divide one by the annual chance. A 2% annual chance is roughly a once-in-fifty-years event. This is the single most useful conversion, because businesses think in years.

Into a portfolio. If you have forty properties and each has a 1-in-40 chance per year, you should expect roughly one event a year, somewhere. Rare for each, routine for the group, which is precisely why insurers can be confident about a book of business while being unable to say anything about your particular building.

Into a century. Draw a hundred squares, one for each year of a century, and shade the ones where you would expect the event. Some risks fill the grid. Some barely mark it.

1 in 10 a year 1 in 100 a year 1 in 1,000 a year nothing to shade About 10 years in a century About 1 year in a century About 1 year in ten centuries Each square is one year. A century of trading, three different risks.
Fig. 5 · The same century, three risks. The first you will meet repeatedly and should plan for as an operating cost. The third you will probably never see, which is not the same as it being impossible.

One warning, because this technique can be abused. A comparison is only honest if it is chosen to inform rather than to win an argument. Telling someone a risk is "less likely than being struck by lightning" is a way of ending a conversation, not a way of explaining it, and it usually gets deployed on exactly the risks that would be most expensive if they landed. Give the waiting time, give the cost if it happens, and let the person decide.

Use it

  • Convert everything to years. Before you make a decision, restate every percentage as "about once every N years." It changes how the number feels, correctly.
  • Ask for both halves. A probability without a cost is half a fact. "Rare but survivable" and "rare but fatal" are different problems.
  • Be suspicious of a lone comparison. If someone reaches straight for lightning strikes, ask what the loss would be if it did happen.

Want this run against your own numbers?

We put ranges, not single figures, against the risks your business actually carries.

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Explanatory content only. This article describes how insurance and risk decisions work in general terms; it is not insurance, legal, actuarial, or investment advice, and it is not a recommendation to buy, keep or cancel any cover. Every figure and diagram is illustrative, chosen to make a mechanism visible, not to describe any particular business.